The values of x and y are 7 and 12 respectively
Solving simultaneous equationsFrom the question, we are to determine the values of x and y
From the given information,
Line AB and Line CD bisect each other at point E
Then, we can conclude that
AE = BE
and
CE = DE
From the given information,
AE = 3x - 10y + 123
BE = -2x - 7y + 122
CE = 9x + 10y - 171
DE = 3x + 20y - 249
Then, we can write that
3x - 10y + 123 = -2x - 7y + 122
Simplifying
3x +2x -10y + 7y = 122 -123
5x -3y = -1 ----------- (1)
Also,
9x + 10y - 171 = 3x + 20y - 249
Simplifying
9x -3x +10y -20y = -249 + 171
6x -10y = -78 --------- (2)
Now, solve equations (1) and (2) simultaneously
5x -3y = -1 ----------- (1)
6x -10y = -78 --------- (2)
Multiply equation (1) by 10 and equation (2) by 3
10 × ( 5x -3y = -1
3 × ( 6x -10y = -78
50x -30y = -10 ----------- (3)
18x -30y = -234--------- (4)
Then, subtracting equation (4) from equation (3), we get
50x -18x -30y-(-30y) = -10-(-234)
32x -30y + 30y = -10 + 234
32x = 224
∴ x = 224/32
x = 7
Put the value of x into equation (1), to find y
5x -3y = -1
5(7) -3y = -1
35 -3y = -1
35 + 1 = 3y
36 = 3y
∴ y = 36/3
y = 12
Hence, the values of x and y are 7 and 12 respectively
Learn more on Solving simultaneous equations here: https://brainly.com/question/148035
#SPJ1
Find the highest common factor of 12 and 40
To find the highest common factor (HCF) between two numbers , first to take HCF of both the numbers.
[tex] \purple {\Large\begin{array}{r | l}2&\underline{12}\\3& \underline{6}\\2&\underline{2}\\&\underline{1}\\\end{array}} \: \: \: \: \: \: \: \: \: \: \: \: \purple {\Large\begin{array}{r | l}2&\underline{40}\\2& \underline{20}\\5&\underline{10}\\2&\underline{2} \ \\ &\underline{1}\\\end{array}}[/tex]
Take every common prime factor between 12 and 40[tex] \red {\large \implies} \large \: 12 \: = \: 2 \: \times \: 3 \: \times \: 2 \: \: \: \: \: \: \: \: \: \: \\ \\ \red {\large \implies} \large \:40 \: = \: 2 \: \times \: 2 \: \times \: 5 \: \times \: 2 \: [/tex]
Finally, identify the factors common to each number and multiply those common factors together.
[tex] \rm\orange {\large \implies} \large \:Common \: factors \: = \: 2 \: \times \: 2[/tex]
[tex]\rm\orange {\large \implies} \large \:HCF = 4[/tex]
Please help me with my math
Answer:
6.4
Step-by-step explanation:
It's stated that the shapes are similar.
We can use similarity ratio to find the value of x:
LM/CD = KL/BA
x/4 = (11.2)/7 cross multiply expressions
7x = 44.8 divide both sides by 7
x = 6.4
Ariana scored 89% out of 600 in Exam what could be the marks she had scored?
Answer:
534
Step-by-step explanation:
The solution is in the image
Raphael is ordering a scoop of ice cream. For the flavor, he is given the option of chocolate, strawberry, vanilla, cookies ‘n cream, or peanut butter. For the size, he is given the option of small, medium, or large. For the cone, he is given the option of a sugar cone, waffle cone, or cup. How many possible order combinations are there?
Answer: 165
Step-by-step explanation: If you calculate the 3 different choices and the total of 11 different objects, you get 165 total combinations.
Answer:
45 possible combinations
Step-by-step explanation:
since there are 5 options of flavour (chocolate, strawberry, vanilla, cookies 'n' cream, and peanut butter) then you must multiply your flavours by your next option.
the size options come in 3 options (small, medium, and large) therefore we multiply the flavours (5) by sizes (3)
5 * 3 = 15
then multiply the result (15) by the cup options (3)
15 * 3 = 45
your answer is 45
hope this helps:)
PLEASE ANSWER ASAP!!!!!!!
a⃗ =<5, −1> and b⃗ =<2,−2>.
Represent a⃗ +b⃗ using the head-to-tail method.
Use the Vector tool to draw a⃗ and b⃗ , complete the head-to-tail method, and draw a⃗ +b⃗
To use the Vector tool, select the initial point and then the terminal point.
(please give picture of graph)
OC represents vector a and b drawn using the head-to-tail method.
What is a Vector ?A vector is an object that has both magnitude and direction.
The given vectors are
a =<5, −1> and b =<2,−2>
Representing vector a +b using the head and tail method
Here in the image attached with the answer ,
The vector a is represented by OA and the vector b is represented by OB
By head and tail method , the OC is drawn by extending the vector a towards b and b towards a
Vector OC = Vector OA + Vector OB
To know more about Vector
https://brainly.com/question/13322477
#SPJ1
What is the slope of the line thatpasses through these two points?(2,3)(2,9)
Answer:
The slope is undefined
Step-by-step explanation:
[tex]m=\frac{9-3}{2-2}[/tex]
The denominator leads to 0 so it would not be possible to find the answer
Answer:
undefined
Step-by-step explanation:
anything divided by zero is undefined since you cant logically give (for example) 2 apples to 0 people.
For slopes not so obvious, the formula is (slope)m= (rise)y/(run)x
convert the following numbers into scientific notation
3,400=
0.000023=
4.50=
1,000,000=
0.00671=
The Scientific notation of given numbers are [tex]3400=3.4 \times 10^{-3}[/tex], [tex]0.000023=2.3 \times 10^{5}[/tex], 4.50, [tex]1,000,000=1 \times 10^{6}[/tex] and [tex]0.00671=6.71 \times 10^{-3}[/tex].
The given numbers are 3400, 0.000023, 4.50, 1,000,000 and 0.00671.
What is scientific notation?Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.
Now, [tex]3400=3.4 \times 10^{-3}[/tex], [tex]0.000023=2.3 \times 10^{5}[/tex], 4.50, [tex]1,000,000=1 \times 10^{6}[/tex] and [tex]0.00671=6.71 \times 10^{-3}[/tex].
Therefore, the Scientific notation of given numbers are [tex]3400=3.4 \times 10^{-3}[/tex], [tex]0.000023=2.3 \times 10^{5}[/tex], 4.50, [tex]1,000,000=1 \times 10^{6}[/tex] and [tex]0.00671=6.71 \times 10^{-3}[/tex].
To learn more about the Scientific notation visit:
https://brainly.com/question/18073768.
#SPJ1
∠C, ∠F are rt. ∠'s; AB = DE; BC = EF
the probability of drawing a diamond or a queen from a pack of 52 cards is
Answer:
25 percent chance or 13/52 for drawing a diamond and 4/52 for a queen
Step-by-step explanation:
There are 13 diamonds in a stack of 52 cards, hence 13/52 or 25 percent chance of drawing a diamond.
Since there are only 4 queens in a stack of 52 cards, so 4 out of 52 cards are queens
how do you write 0.8 recurring as a fraction?
please can i have an explanation aswell :)
Answer:
[tex]\frac{8}{9}[/tex]
Step-by-step explanation:
we require 2 equations with the repeating digits placed after the decimal point.
let x = 0.888.. (1) ← multiply both sides by 10
10x = 8.888.. (2)
subtract (1) from (2) thus eliminating the repeating digits
9x = 8 ( divide both sides by 9 )
x = [tex]\frac{8}{9}[/tex]
Find the values of a and b 3 * 2 = a + b if
value of a = 3
value of b = 2
a + b = 3 + 2 = 5 .
Quick I need an answer to this Queston:
The functions f(x)= −3/4x + 2 1/4 and g(x)= (1/2)x + 1 are shown in the graph.
What are the solutions to −3/4x + 2 1/4 = (1/2)x + 1?
Select each correct answer.
−1
0
1
2
3
Step-by-step explanation:
[tex] - \frac{3}{4} x + 2 \frac{1}{4 } = \frac{1}{2} x + 1[/tex]
[tex] - \frac{3}{4} x + \frac{9}{4} = \frac{1}{2} x + \frac{2}{2} [/tex]
[tex] \frac{ - 3x + 9}{4} = \frac{2x + 4}{4} [/tex]
[tex] - 3x + 9 = 2x + 4[/tex]
[tex] - 3x - 2x = 4 - 9[/tex]
[tex] - 5x = - 5[/tex]
[tex]x = \frac{ - 5}{ - 5} [/tex]
[tex]x = 1[/tex]
The answer is C.
9.
Let f(x) = 2x + 2. Solve f−1(x) when x = 4. (1 point)
Answer:
1
Step-by-step explanation:
The value of the output given by the inverse for a given input is the same as the input of the original function that results in the output equal to the given input.
So, 2x + 2 = 4, meaning the answer is 1
It takes two points to define a plane.
Answer:
In a Euclidean space of any number of dimensions, a plane is uniquely determined by any of the following: Three non-collinear points (points not on a single line). A line and a point not on that line. Two distinct but intersecting lines.
Step-by-step explanation:
please mark me brainlist and follow me
Construct a rectangle with sides 6cm and 4cm.
Answer:
Step-by-step explanation:
Answer:
First, draw a line segment AB = 6 cm.Draw a ray AX with pencil and compass such that ∠BAX = 90°. Draw an arc of 4 cm with point A which intersects AX at D.Similarly, draw ray BY such that ∠ABY = 90°. Draw an arc of 4 cm with point B which intersects BY at C.Join CD.Thus ABCD is the required rectangle.find the area of quadrilateral
Answer:
here is answer try this type
Step 3: So, M 12= 60 Degrees
Use the drop-down menus to explain whether or not Stuart is corrrect.
The reasoning that may be used for finding the measure of m∠12, is the
same side interior angles theorem.
The correct options using the drop-down menu are;
The sum of ∠1, ∠7, and ∠8 is 180°
∠8 and ∠12 are the same side interior angles
The measure of ∠12 must be = 120°
Stuart is not correct
The complete question is given below:-
In the diagram, line x is parallel to line y,m21= 65°, and m27 = 55°. Stuart says that m212 = 60°. His reasoning is shown. Step 1: mZ8 = 60°, because m21+ m27 +m28 = 180º. Step 2:28 212, because 28 and 212 are corresponding angles. Step 3: So, mZ12 = 60° Use the drop-down menus to explain whether or not Stuart is correct.
What is an angle?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
Given parameters;
Line x ║ line y
m∠1 = 65°, m∠7 = 55°
m∠12 = 60°
Stuart states ∠12 = 60°
The reasoning is presented as follows;
Step 1: m∠8 = 60°, because m∠1 + m∠7 + m∠8 = 180°
Step 2: ∠8 ≅ ∠12, because ∠8 and ∠12 are corresponding angles
Step 3: So, m∠12 = 60°
Using the drop-down menu, we have;
The sum of ∠1, ∠7, and ∠8 is 180° (Sum of angles in the triangle)
∠8 and ∠12 are same side interior angles (by definition)
Same side interior angles are supplementary, therefore;
∠8 +∠12 = 180°
∠12 = 180° - ∠8
Which gives;
The measure of ∠12 must be 180° - ∠8 = 180° - 60° = 120°
The measure of ∠12 must be = 120°
Stuart is not correct
To know more about an angle follow
https://brainly.com/question/25770607
#SPJ1
The directrix and focus of a parabola are shown on the graph. Which is an equation for the parabola?
Find one-third of the sum 9 and 12.
Answer:
7
Step-by-step explanation:
9 plues 12 = 21
21 divide by 3
= 7
Answer:
7
Step-by-step explanation:
9 + 12 = 21
one third of 21 is the same as 21 divided by 3
so 21 divided by 3
= 7
so 7 is the answer
OR
9 divided by 3 = 3
12 divided by 3 = 4
3 + 4 = 7
in january of 2013, mr edwards turned 64 years old. in what year was mr edwards born.
Answer:
xhdvuvzxvzvkkzv jzh jhj,
Step-by-step explanation:
ΔXYZ was reflected over a vertical line, then dilated by a scale factor of One-half, resulting in ΔX'Y'Z'. Which must be true of the two triangles? Select three options.
The options that are true of the triangles include:
∆XYZ ~∆X'Y'Z'AngleXZY ≅ AngleY'Z'X'XZ = 2X'Z'The complete question is given below:-
ΔXYZ was reflected over a vertical line, then dilated by a scale factor of One-half, resulting in ΔX'Y'Z'. Which must be true of the two triangles? Select three options.
△XYZ ~ △X'Y'Z'AngleXZY ≅ AngleY'Z'X'YX ≅ Y'X'XZ = 2X'Z'mAngleYXZ = 2mAngleY'X'Z'What is translation?The process of changing the location of the image on the coordinate system will be known as the translation.
It should be noted that triangle XYZ is reflected over a vertical line. Then, it's dilated by 1/2 to form XYZ.
This implies that the triangles are similar, the angles are congruent and the side length of XYZ is twice that of X'Z.
Therefore the options that are true of the triangles include:
∆XYZ ~∆X'Y'Z'AngleXZY ≅ AngleY'Z'X'XZ = 2X'Z'Learn more about translation on:
https://brainly.com/question/12861087
#SPJ1
Helppp will give brainliest
Let x1 = 21, y1 = −15, and y2 = 9, and let y vary inversely as x. Find x2.
Answer:
The value of [tex]x_{2}[/tex] from inverse variation is (-35).
Step-by-step explanation:
Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases. While direct variation describes a linear relationship between two variables, inverse variation describes another kind of relationship.
An inverse variation can be represented by the equation
xy=k .
That is y varies inversely as x if there is some nonzero constant k.
Here, the product is given by :
x1y1=x2y2
21 x (-15)=x2 x 9
(-315) / 9 = x2
x2=(-35)
Learn more about inverse variation - https://brainly.com/question/2798700
#SPJ10
i would appreciate your help
__________________________________________________________
[tex]\text{\textbf{Hello!} In this question, we are trying to figure out the \underline{equation} of the line}\\\text{with the given information.}[/tex]
__________________________________________________________
[tex]\textbf{Explanation:}\\\quad{}\\\text{In the question, we were given our \emph{slope} (gradient) and a \emph{point}. This will help}\\\text{us solve our problem.}\quad{}\\\\\text{Slope: 2 }\\\\\text{Point: (1, 4)}\\\quad{}\\\text{In order to find the equation, we will be using the \underline{point-slope formula:}}\\\quad{}\\y - y1 = m(x - x1)\\\quad{}\\\text{With this equation, we would plug in our given values to its}\\\text{correct variable and solve.}[/tex]
__________________________________________________________
[tex]\textbf{Solve:}\\\\\text{Use the point-slope formula to solve.}\\\\y - y1 = m(x - x1)\quad{}\\\\\text{Plug in 2 to m, 1 to x1, 4 to y1 and then solve.}\\\\y - 4 = 2(x - 1)\\\\\text{Use the \underline{distributive property} to distribute the 2.}\\\\y - 4 = 2x - 2\\\\\text{Add 4 to both sides to cancel the 4 on the left and move the remainder}\\\text{to the right side of the equal sign.}\\\\y = 2x + 2\\\\\text{Since we can't simplify any further, our answer is: \fbox{y = 2x + 2}}[/tex]
__________________________________________________________
[tex]\textbf{Answer:}\\\\\text{Therefore, the equation of the line (our final answer) would be \fbox{y = 2x + 2}}[/tex]
__________________________________________________________
Please help me asap 5/11
By applying concepts related to matrices and their dimensions, the element of the matrix that belongs to the 2nd row and 3rd column is 6.
How to determine the content associated to the index of a matrix
Matrices are constructions studied by linear algebra, are a particular case of tensors. This kind of constructions are characterized by two dimensions: (i) Number of rows - Horizontal rows, (ii) Number of columns - Vertical rows.
Each element of an matrix A has an associated index with the following form:
[tex]a_{i,j}[/tex]
Whose meaning is "element of the matrix A that belongs to the i-th row and j-th column".
In this case, we find that the element of the matrix that belongs to the 2nd row and 3rd column is 6.
To learn more on matrices: https://brainly.com/question/11367104
#SPJ1
The following two way table shows the number of students of a school who have a cell phone and or have a part-time job.
Answer:
the answer is b.40 that the kids that are working and have phone b
what is the solution to square root 5x+3= 3 square root x?
A.3/4
B. 3/2
C.-3/4
D.-3/2
Answer:
A. 3/4
Step-by-step explanation:
1. Square both sides:
5x + 3 = 9x
2. Subtract 5x from both sides:
3 = 4x
3. Divide 4 from both sides:
3/4 = x
Answer: A
Answer:
3/4
Step-by-step explanation:
it's correct
Brian ordered 3 large cheese pizzas and a salad. The salad cost $4.95. If he spent a total of $47.60 including the $5 tip, how much did each pizza cost? (Considering there's no tax) Please I really need help
Answer:
Each pizza was $12.55.
Step-by-step explanation:
et's take it piece by piece.
Salad and the tip together is 4.95 + 5 = 9.95, right?
47.60 - 9.95 = 37.65 spent on pizza
37.65/3 = 12.55
how many eggs are in 2 3/4 dozen?
please answer this one...i need it today
Step-by-step explanation:
please mark me as brainlest
Answer:
33 eggs
Step-by-step explanation:
1 Dozen = 12 units
2 dozen = 2*12 = 24 units
3/4 dozen = 12*3/4 = 36/4 = 9 units
2 3/4 = 2 + 3/4 = 24 + 9 = 33 units
Can someone explain to me #2 I only need #2
Answer:
in a rectangle, opposite sides are equal in length
Step-by-step explanation:
now in this question, Pythagoras theorem is being used to find the length
we know both sides by using Pythagoras theorem find third side and get the sum to find ac+bd
Step-by-step explanation:
So it tells you that AB = 21 and AD = 28
and you to find what BD + AC is and since BD is the same length as AC
you only need to find one of them, then double it
There is a formula you use called the Pythagorean theorem
The Pythagorean theorem is A²+B²=C²
In this problem A = 21 B = 28 and C = the length of BD
so it'll look like 21²+28²=Length of BD² or BD²=21²+28² now you find BD
first do 21²+28² --> 441+784 --> 1225 Now you know that 21²+28²=1225
so BD²=1225 Then to find BD, you find √1225(square root of 1225)
Which is 35 So BD=35 and you want to know what BD+AC is
so 35+35=70
The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 37 hours and the median is 33.2 hours. Twenty-four of the families in the sample turned on the television for 22 hours or less for the week. The 10th percentile of the data is 22 hours. Based on the given information, determine if the following statement is true or false. Approximately 120 families turned on their televisions for less than 37 hours.
The statement; Approximately 120 families turned on their televisions for less than 37 hours is true.
What is true about the data?From the task content, since the 10% percentile of the data corresponds to 24 families, it.follws that the total number of families sampled is; 24 × 10 = 240 families.
On this note, after the first 120 data points, the median is determined to be 33.2 hours which is less than the mean. Conclusively, it follows that approximately 120 families turned on their televisions for less than 37 hours.
Hence, the statement is true.
Read more on median and mean;
https://brainly.com/question/14532771
#SPJ1